Commutative Stochastic Games

• 成果类型: Article
• 署名作者: Venel, Xavier
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - Institute for Humanities & Social Sciences (INSHS); heSam Universite; Universite Pantheon-Sorbonne
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2014.0676
• 发表日期: 2015
• 页码: 403-428
• 关键词: Incomplete information

摘要

We are interested in the convergence of the value of n-stage games as n goes to infinity and the existence of the uniform value in stochastic games with a general set of states and finite sets of actions where the transition is commutative. This means that playing an action profile a(1) followed by an action profile a(2), leads to the same distribution on states as playing first the action profile a(2) and then a(1). For example, absorbing games can be reformulated as commutative stochastic games. When there is only one player and the transition function is deterministic, we show that the existence of a uniform value in pure strategies implies the existence of 0-optimal strategies. In the framework of two-player stochastic games, we study a class of games where the set of states is R-m and the transition is deterministic and 1-Lipschitz for the L-1-norm, and prove that these games have a uniform value. A similar proof shows the existence of an equilibrium in the nonzero-sum case. These results remain true if one considers a general model of finite repeated games, where the transition is commutative and the players observe the past actions but not the state.